Willingness to Pay for Clean Air: Evidence from Air Purifier Markets in China

Demand for Air Purifiers

Random Utility Model

• Consumer i in city c can purchase air purifier j at price p_{jc} to reduce indoor air pollution by x_{jc} = x_c \cdot e_j
• Purifier j’s effectiveness at reducing indoor particulate matter e_j \in [0,1]
• Observe markets for c = 1,...,C cities with i=1,...,I_c consumers

Then the conditional indirect utility of consumer i from purchasing air purifier j at city c is

u_{ijc} = \beta_i x_{jc} + \alpha_i \rho_{jc} + \eta_j + \lambda_c + \xi_{jc} + \epsilon_{ijc}

where x_{jc} represents the improvements in indoor air quality conditional on the purchase of product j, \rho_{jc} represents the price of product j in market c, \eta_j represents product fixed effects that capture utility gains from unobserved and observed product characteristics, \lambda_c represents city fixed effects, \xi_{jc} represents a product-city specific demand shock, and \epsilon_{ijc} represents a mean-zero stochastic term.

• \beta_i: marginal utility for clean air
• \alpha_i: marginal disutility of price

Demand for Air Purifiers

Logit Model

Assuming that \beta_i = \beta and \alpha_i = \alpha for consumer i and that the error term is distributed as a type I extreme value function, then consumer i purchases purifier j if u_{ijc} > u_{ikc} for \forall k \ne j. Then the market share for product j in city c is

s_{jc} = \frac{\exp \left( \beta x_{jc} + \alpha p_{jc} + \eta_j + \lambda_c + \xi_{jc} \right)}{\sum_{k=0}^{J} \exp \left( \beta x_{kc} + \alpha p_{kc} + \eta_k + \lambda_c + \xi_{kc} \right)}

which simplifies to

\begin{align*} s_{jc} &= \beta x_{jc} + \alpha \rho_{jc} + \eta_j + \lambda_c + \xi_{jc} \\ s_{jc} &= \beta x_{c} H_j + \alpha \rho_{jc} + \eta_j + \lambda_c + \xi_{jc} \end{align*}

• x_{c}: ambient pollution
• H_j: indicator variable for HEPA purifiers
• Identifying variation: x_{c} H_j has city-by-product variation and \rho_{jc} has city-by-product

Empirical Strategy

RD

First Stage:

x_c = \gamma N_c + \phi_1 d_c + \phi_2 d_c N_c + \nu_l + \epsilon_c

where x_c represents PM₁₀ in city c, N_c is the dummy variable for the north, d_c represents the distance between city c and the Huai River, and e_c is the error term.

• \nu_l measures a discontinuous change in x_c at the Huai River border

Reduced form RD: \ln s_{jc} = \rho N_c H_j + \alpha p_{jc} + \left( \psi_1 d_c + \psi_2 d_c N_c + \nu_l \right) H_j + \eta_j + \lambda_c + \epsilon_{jc}

where s_{jc} and p_{jc} respectively represent the market share and the price of product j in city c, \eta_j represents product fixed effects, and \lambda_c represents city fixed effects.